The Fiji Mermaid, often ranked today as one of the top ten science hoaxes, was a hoax exhibited by P.T. Barnum at sideshows. It was later revealed to be a top half of a monkey sewn onto the bottom half of a fish, and rather artlessly at that.
However, one need not think that early beliefs in mermaids were entirely founded by superstition; there is a rare congenital birth deformity known as Sirenomelia, in which a baby is born with the legs fused together.
A post about it here, but be warned, some photos are shocking. And Googling the name in images isn't advised for the nervous, either.